A high speed train is traveling at a speed of 44.7 m/s when the engineer sounds the 415 Hz warning horn. The speed of sound is 343 m/s. What is the wavelength of the sound, as perceived by the person standing at a crossing when the train is a) approaching and b) find the frequency when leaving the crossing?

Speed of the source of sound = v = 44.7 m/s

Speed of sound = V = 343 m/s

a) Apparent frequency as the train approaches = f = [V / (V - v) ] * f

= [343 / (343 - 44.7) ] * 415 = 477.18 Hz

Wave length = λ = v / f = 343 / 477.18 = 0.719 m

b) Frequency heard as the train leaves = f ' = [V / (V + v) ] f

= [343 / { 343 + 44.7) ] x 415

= 367.2 Hz

Wavelength when leaving = v / f = 343 / 367.2 = 0.934 m